Max Planck Institute for Dynamics and Self-organization, Am Faßberg 17, 37077 Göttingen, Germany.

Laboratoire de Physique de l'École Normale Supérieure (PSL University), CNRS, Sorbonne Université, and Université de Paris, 75005 Paris, France.

Memorial Sloan Kettering Cancer Center, New York, New York 10065, USA.

Department of Physics, University of Washington, 3910 15th Avenue Northeast, Seattle, Washington 98195, USA.

Fred Hutchinson cancer Research Center, 1100 Fairview ave N, Seattle, Washington 98109, USA.

T-cell receptors (TCR) are key proteins of the adaptive immune system, generated randomly in each individual, whose diversity underlies our ability to recognize infections and malignancies. Modeling the distribution of TCR sequences is of key importance for immunology and medical applications. Here, we compare two inference methods trained on high-throughput sequencing data: a knowledge-guided approach, which accounts for the details of sequence generation, supplemented by a physics-inspired model of selection; and a knowledge-free variational autoencoder based on deep artificial neural networks. We show that the knowledge-guided model outperforms the deep network approach at predicting TCR probabilities, while being more interpretable, at a lower computational cost.